CPU Time Savings Research Articles

Implementation and performance of a domain-specific basis set incremental approach for correlation energies: Applications to hydrocarbons and a glycine oligomer

The fully automated implementation of the incremental scheme for CCSD energies has been modified for the usage of a domain-specific basis set. We find that the computational effort can be reduced significantly without loss of accuracy. It is shown explicitly in applications on hydrocarbons and the (glycine)(4) oligomer that the error of the incremental expansion for the total energy is usually below 1 kcal/mol at third order. Furthermore, it is demonstrated that the proposed approach saves CPU time, random access memory, and disk space. Moreover, we show in various tests that the inherently parallel incremental calculations can be run on up to 50 CPUs without significant loss of computer time.

Paradigmatic flow for small-scale magnetohydrodynamics: Properties of the ideal case and the collision of current sheets

We propose two sets of initial conditions for magnetohydrodynamics (MHD) in which both the velocity and the magnetic fields have spatial symmetries that are preserved by the dynamical equations as the system evolves. When implemented numerically they allow for substantial savings in CPU time and memory storage requirements for a given resolved scale separation. Basic properties of these Taylor-Green flows generalized to MHD are given, and the ideal nondissipative case is studied up to the equivalent of 2048;{3} grid points for one of these flows. The temporal evolution of the logarithmic decrements delta of the energy spectrum remains exponential at the highest spatial resolution considered, for which an acceleration is observed briefly before the grid resolution is reached. Up to the end of the exponential decay of delta , the behavior is consistent with a regular flow with no appearance of a singularity. The subsequent short acceleration in the formation of small magnetic scales can be associated with a near collision of two current sheets driven together by magnetic pressure. It leads to strong gradients with a fast rotation of the direction of the magnetic field, a feature also observed in the solar wind.

Generation of Aerodynamics Databases Using High-Order Singular Value Decomposition

The fast generation of aerodynamic databases is important in the aeronautic industry because of its implication on both the cost and time needed to complete design cycles. This paper presents a method of generating those databases that uses a limited number of computational fluid dynamics computations, thereby saving CPU time. The method is based on a high-order singular value decomposition approach and is able to deal efficiently with complex airfoil flowfields that contain, simultaneously, two shock waves and a large separation region. This feature is critical because methods based on the singular value decomposition approach tend to encounter difficulties when dealing with shock wavelike structures. To illustrate the methodology, the flow around a two-dimensional airfoil is considered at a Reynolds number of 20 ×10 6 with three free parameters, namely, the Mach number, angle of attack, and flap deflection angle in the ranges of 0.4-0.8, -3- + 3 deg, and -5- + 5 deg, respectively. The method is robust in the sense that it is able to deal with very different flow topologies. Also, it is expected that it will contribute to significant savings in CPU time in aerodynamic database generation activities.

Effects of some parameters on numerical simulation of coastal bed morphology

PurposeThe aim is to investigate in detail the sensitivity of sediment transport and bed morphology with respect to some parameters including bed slope, non‐hydrostatic pressure term, sand grain size, temperature, salinity and lower boundary conditions for suspended sand concentration on a regional scale through numerical simulations based on a mathematical model.Design/methodology/approachThe numerical model consists of a 3D hydrodynamic code amended by a sediment transport module. At the same time, the influence of wave action has been taken into account. The model is applied to the Sylt‐Romo tidal bay covering approximately 20 × 30 km2 spanned by about 2.7 × 106 active grid points with the constant wind and wave fields.FindingsThe computed results of seven different cases over 150 h show that the effect of bed slope correction is very strong, especially in case of largely changeable bathymetry and depends on the horizontal grid resolution. Sand grain size strongly influences the vertical distribution of suspended sediment and then sedimentation. The impact of sea water temperature is relatively clear despite being less powerful than two former parameters. Non‐hydrostatic pressure perturbations of the flow field and the kind of the lower boundary condition as well as salinity are negligible allowing for considerable savings of CPU time when the numerical simulation is carried out for a large area and for a very long‐time period.Originality/valueThe results of the study demonstrate that the geometrical factor of coastal bed and the range of sand particle size on the bottom contribute to the tendency of bed evolution in some measure. Additionally, the increase of temperature of sea water due to global warming may also make a considerable change to the mechanism of sediment transport and sedimentation in future. Therefore, the human intervention in the process of natural evolution is possible through the behaviour to the nature. At the same time, this is also interesting and useful information and it can consolidate the idea for coastal engineering projects.

A New Conformal FDTD(2,4) Scheme for Modeling Three-Dimensional Curved Perfectly Conducting Objects

A new high-order conformal FDTD(2,4) scheme is proposed to solve the electromagnetic scattering from 3-D curved perfectly conducting objects. For electric field components, the update equations do not need to be modified. For magnetic field components, the inner loop is treated with the locally conformal technique, and the outer loop is unmodified. Numerical results demonstrate that the high-order conformal scheme can obtain better numerical precision under coarse grid condition compared with the low-order conformal method and the high-order staircasing approach, which in turn saves CPU time and memory.

RCM‐TVD hybrid scheme for hyperbolic conservation laws

AbstractWe describe a hybrid method for the solution of hyperbolic conservation laws. A third‐order total variation diminishing (TVD) finite difference scheme is conjugated with a random choice method (RCM) in a grid‐based adaptive way. An efficient multi‐resolution technique is used to detect the high gradient regions of the numerical solution in order to capture the shock with RCM while the smooth regions are computed with the more efficient TVD scheme. The hybrid scheme captures correctly the discontinuities of the solution and saves CPU time. Numerical experiments with one‐ and two‐dimensional problems are presented. Copyright © 2007 John Wiley & Sons, Ltd.

Behavior of density functionals with respect to basis set. VI. Truncation of the correlation consistent basis sets

Systematic truncation of the correlation consistent basis sets has been investigated in first and second row atoms and molecules to better understand basis set requirements for density functional theory, particularly the need for high angular momentum functions, as well as to understand possible computational cost savings that could be achieved by using reduced basis sets. The truncation scheme employed follows that recently introduced for ab initio methods [B. Mintz et al., J. Chem. Phys. 121, 5629 (2004)]. Properties examined in the current study include geometries, ionization potentials, electron affinities, and dissociation energies. In general, this investigation shows that a degree of truncation of higher angular momentum functions is possible with limited impact upon energetic properties, and does result in useful CPU time savings. However, not all properties investigated have the same level of dependence upon high angular momentum functions, and, thus, careful selection of truncated basis sets should be made.

Efficient calculation of the history force at finite Reynolds numbers

Well-acknowledged problems associated with modeling the history force in large, many-particle simulations are related to the need to store and integrate over the entire lifetime of the particle. To address this concern, a computationally efficient method for calculating the history force (the “window model”) was developed based on the assumption of weak changes in acceleration in the recent relevant history of the particle. This assumption leads to the design of a model with a truncated integration interval which requires storage of and integration over a much shorter period of the particle’s history compared to other history force models. The truncation of the integration window can yield more than an order of magnitude savings in CPU time. In a related study, the two empirical coefficients of the Mei & Adrian history force kernel have been optimized (based on comparison with experimental data for falling particles) to give improved predictions of the data. Both the new history force kernel and the window model have been investigated for a large range of experimental data yielding, to the authors’ knowledge, the most extensive comparison yet conducted. For falling particles, the new history force kernel shows good predictions for particle Reynolds numbers ranging from 9 to 853 and density ratios from 1.17 to 9.32. Good predictions were also obtained using the window model when changes in particle relative acceleration over the window period were modest. For particles under forced oscillating in a quiescent fluid, the history kernel was generally reasonable but did not predict the peak forces well in all cases. This may be explained by noting that the assumption of a t −2 long-time dependence for the finite Reynolds number history force kernel may become invalid during rapid deceleration and wake ingestion (which can lead to exponential or t −1 behavior). However, the finite Reynolds number kernel gives better predictions in all cases than those made using the Basset history force. The window model was only reasonable for the oscillating particle cases when the changes in the relative particle acceleration over the integration window were small.

Electromagnetic optimisation using sensitivity analysis in the frequency domain

Gradient-based optimisation relies on the response Jacobian whose evaluation constitutes a major computational overhead in full-wave numerical analysis. Adjoint-based techniques may offer numerically efficient solutions, but their implementation is too involved in the case of full-wave computations. A simple approach that uses the self-adjoint sensitivity analysis and Broyden's update is proposed. The overhead of the Jacobian computation is greatly reduced because an adjoint system analysis is not needed and because Broyden's update is used to compute the system matrix derivatives. To improve the robustness of the Broyden update in the sensitivity analysis, we propose a switching criterion between the Broyden and the finite-difference estimation of the system matrix derivatives. We illustrate and validate the proposed method using full-wave commercial electromagnetic solvers based on the finite-element method as well as on the method of moments. Different gradient-based optimisation algorithms are exploited in the examples where efficiency is compared in terms of CPU time savings.

Efficiency of a POD‐based reduced second‐order adjoint model in 4D‐Var data assimilation

AbstractOrder reduction strategies aim to alleviate the computational burden of the four‐dimensional variational data assimilation by performing the optimization in a low‐order control space. The proper orthogonal decomposition (POD) approach to model reduction is used to identify a reduced‐order control space for a two‐dimensional global shallow water model. A reduced second‐order adjoint (SOA) model is developed and used to facilitate the implementation of a Hessian‐free truncated‐Newton (HFTN) minimization algorithm in the POD‐based space. The efficiency of the SOA/HFTN implementation is analysed by comparison with the quasi‐Newton BFGS and a nonlinear conjugate gradient algorithm. Several data assimilation experiments that differ only in the optimization algorithm employed are performed in the reduced control space. Numerical results indicate that first‐order derivative methods are effective during the initial stages of the assimilation; in the later stages, the use of second‐order derivative information is of benefit and HFTN provided significant CPU time savings when compared to the BFGS and CG algorithms. A comparison with data assimilation experiments in the full model space shows that with an appropriate selection of the basis functions the optimization in the POD space is able to provide accurate results at a reduced computational cost. The HFTN algorithm benefited most from the order reduction since computational savings were achieved both in the outer and inner iterations of the method. Further experiments are required to validate the approach for comprehensive global circulation models. Copyright © 2006 John Wiley & Sons, Ltd.

Propagation of Ultra–High‐Energy Cosmic Rays above 1019eV in a Structured Extragalactic Magnetic Field and Galactic Magnetic Field

We present numerical simulations of the propagation of ultra-high-energy cosmic rays (UHECRs) above 1019 eV in a structured extragalactic magnetic field (EGMF) and simulate their arrival distributions at the Earth. We use the IRAS PSCz catalog in order to construct a model of the EGMF and source models of UHECRs, both of which reproduce the local structures observed around the Milky Way. We also consider modifications of UHECR arrival directions by the Galactic magnetic field. We follow an inverse process of their propagation from the Earth and record the trajectories. This enables us to calculate only trajectories of UHECRs arriving at the Earth, which saves CPU time. From these trajectories and our source models, we construct arrival distributions of UHECRs and calculate their harmonic amplitudes and two-point correlation functions. We estimate the number density of sources that best reproduces the Akeno Ground Air Shower Array (AGASA) observation. As a result, we find that the most appropriate number density of the sources is ~5 × 10-6 Mpc-3. This constrains the source candidates of UHECRs. We also demonstrate sky maps of their arrival distribution with the event number expected by future experiments and examine how the EGMF affects their arrival distribution. A main result is the diffusion of clustering events, which are obtained from calculations in the absence of the EGMF. This tendency allows us to reproduce the observed two-point correlation function better.

Development of a Semi-implicit Solver for Detailed Chemistry in Internal Combustion Engine Simulations

An efficient semi-implicit numerical method is developed for solving the detailed chemical kinetic source terms in internal combustion (IC) engine simulations. The detailed chemistry system forms a group of coupled stiff ordinary differential equations (ODEs), which presents a very stringent time-step limitation when solved by standard explicit methods, and is computationally expensive when solved by iterative implicit methods. The present numerical solver uses a stiffly stable noniterative semi-implicit method. The formulation of numerical integration exploits the physical requirement that the species density and specific internal energy in the computational cells must be non-negative, so that the Lipschitz time-step constraint is not present and the computation time step can be orders of magnitude larger than that possible in standard explicit methods. The solver exploits the characteristics of the stiffness of the ODEs by using a sequential sort algorithm that ranks an approximation to the dominant eigenvalues of the system to achieve maximum accuracy. Subcycling within the chemistry solver routine is applied for each computational cell in engine simulations, where the subcycle time step is dynamically determined by monitoring the rate of change of concentration of key species, which have short characteristic time scales and are also important to the chemical heat release. The chemistry solver is applied in the KIVA-3V code to diesel engine simulations. Results are compared to those using the CHEMKIN package, which uses the VODE implicit solver. Good agreement was achieved for a wide range of engine operating conditions, and 40-70% CPU time savings were achieved by the present solver compared to the standard CHEMKIN.

Second‐order interpolation of later‐arrival traveltimes

ABSTRACTThe performance of a 3D prestack migration of the Kirchhoff type can be significantly enhanced if the computation of the required stacking surface is replaced by an efficient and accurate method for the interpolation of diffraction traveltimes. Thus, input traveltimes need only be computed and stored on coarse grids, leading to considerable savings in CPU time and computer storage. However, interpolation methods based on a local approximation of the traveltime functions fail in the presence of triplications of the wavefront or later arrivals. This paper suggests a strategy to overcome this problem by employing the coefficients of a hyperbolic traveltime expansion to locate triplications and correct for the resulting errors in the interpolated traveltime tables of first and later arrivals.

Approximating Coupled Cluster Level Vibrational Frequencies with Composite Methods

An extensive study of the harmonic frequencies of a large set of small polyatomic closed-shell molecules computed at both single level ab initio and composite approximations is presented here. Using various combinations of basis sets, composite methods are capable of predicting single level ab initio CCSD(T) harmonic frequencies to within 5 cm(-1) on average, which suggests a computationally affordable means of obtaining highly accurate vibrational frequencies compared to the CCSD(T) level. A general approach for calculating the composite level equilibrium geometries and harmonic frequencies for polyatomic systems that uses the Collin's method of interpolating potential energy surfaces is also described here. This approach is further tested on tetrafluoromethane, and an estimation of the potential CPU time savings that may be obtained is also presented. It is envisaged that the findings here will enable theoretical studies of fundamental frequencies and energetics of significantly larger molecular systems.

A segregated method for compressible flow computation. Part II: general divariant compressible flows

Typically, segregated methods have been used for the computation of incompressible flows whereas coupled solvers, for compressible flows. Compared to coupled solvers, segregated methods present the advantage of computational savings in RAM memory and CPU time, although at the cost of an inferior robustness. However, previously published segregated algorithms for general compressible flows are known to present pitfalls, like convergence to wrong solutions, lack of robustness in the presence of strong discontinuities, such as normal and oblique shocks, and complicated boundary condition imposition. Therefore, a segregated method for non-isothermal compressible flows is proposed that preserves the thermodynamic coupling and overcomes the criticisms of existing methods.

Spatially adaptive lattice coarse-grained Monte Carlo simulations for diffusion of interacting molecules

While lattice kinetic Monte Carlo (KMC) methods provide insight into numerous complex physical systems governed by interatomic interactions, they are limited to relatively short length and time scales. Recently introduced coarse-grained Monte Carlo (CGMC) simulations can reach much larger length and time scales at considerably lower computational cost. In this paper we extend the CGMC methods to spatially adaptive meshes for the case of surface diffusion (canonical ensemble). We introduce a systematic methodology to derive the transition probabilities for the coarse-grained diffusion process that ensure the correct dynamics and noise, give the correct continuum mesoscopic equations, and satisfy detailed balance. Substantial savings in CPU time are demonstrated compared to microscopic KMC while retaining high accuracy.

Solids modeled by ab initio crystal field methods, part 22: the Fock matrix transformed supermolecule model and the structure determination of D-erythronic acid-3,4-carbonate.

To eliminate the cutoff effects in the supermolecule model (SM), the Fock matrix transformed supermolecule model (FTSM) is developed. In this model a cyclization of the cluster is performed by means of transformations of elements of the Fock matrix, thereby restoring the translational symmetry. Besides this fundamental enhancement, significant CPU time savings are realized because, in this new procedure, not all Fock matrix elements need to be calculated. The method is applied in a study of the structure of D-erythronic acid-3,4-carbonate in the crystal phase, where the new model is compared to the supermolecule model as well as the XRD experiment. The results are found to be in good agreement with experimental data.

Finely discretized lattice simulations of SPC/E water

In this work, it is shown that the similarities between discretized and continuum models of water are heavily dependent upon the exact value of the discretization parameter, ζ, defined as the ratio of the Lennard–Jones size parameter σ to the lattice spacing. For example, some discretized models layered into a hexagonal ice-like structure at temperatures up to 550 K. A discretization parameter of ζ = 13 was chosen such that the radial distribution function of the liquid at 298 K for the lattice model closely matched the continuum. This discretized model is capable of reproducing the low-temperature phase diagram with the advantage of significant CPU time savings.

HNS

This article was motivated by the need to speed up complex network simulation, especially in telecommunications settings, where high bandwidth translates into exorbitant numbers of packets that take inordinate CPU time to simulate. Since the simulation complexity of fluid workload is invariant under bandwidth scaling, flows of discrete units of workload may be replaced by (approximate) fluid streams for savings in CPU time and memory storage.To this end, the article outlines the design of a new hybrid Java simulator, called HNS ( Hybrid Network Simulator ). HNS simulates the movement of workload in a queueing network, where transactions may be of two types: traditional discrete transactions (e.g., packets) and continuous (fluid) transactions, all of which arrive discretely at the network in traffic flows, and each discrete arrival carries a workload. Arriving transactions only differ in the way their workloads are transported: the user specifies whether the workload should be packetized or fluidized , respectively, for transport across the network. The novel feature of HNS is that it admits models with both discrete and continuous traffic flows, and collects detailed statistics for both, including arrival, loss, buffer contents, departure, and delay statistics. HNS facilitates the fundamental tradeoff between the modeling accuracy of discrete flows and savings in simulation time and storage often afforded by continuous flows by providing a common testbed for both discrete and continuous flows, where the user can readily select transport modes and achieve a good deal of variance reduction in assessing the accuracy and speeds of model versions with different mixtures of flow types. We caution, however, that while HNS is a generic hybrid simulator of discrete and continuous flows, mixed models should be handled with care, since they tend to counteract the advantages of pure-packet or pure-fluid models.In order to achieve a high degree of speedup for fluid-flow models, HNS introduces and utilizes the so-called streamlining methodology to identify and modify algorithms that cause "turbulent" fluid flow (namely, scenarios where fluid-flow rates have a large number of minor fluctuations, which are computationally expensive but have a minor impact on simulation statistics). Streamlining removes these fluctuations so as to speed up the simulation at a moderate loss of statistical accuracy. HNS can be extended by writing additional Java classes; in particular, stream behavior can be modified by extending built-in protocol classes. For example, HNS already has dual implementations (packet and fluid) of various telecommunications-specific protocols, such as ATM (Asynchronous Transfer Mode), User Datagram Protocol (UDP), and TCP (Transport Control Protocol), the latter with a streamlined fluid protocol approximation.In this article, we describe the architecture of HNS and its operational features, including traffic injection at network sources, generic workload transport, some telecommunications-specific protocols, and statistics collection and display via a graphic user interface (GUI). We then use HNS to validate the streamlining methodology and to study appropriate tradeoffs of simulation speed and accuracy in telecommunications networks by comparing pure-packet, pure-fluid, and mixed versions of the same network model.

Application of the biorthogonal multiresolution time-domain method to the analysis of elastic-wave interactions with buried targets

The biorthogonal multiresolution time-domain (Bi-MRTD) method is introduced for the analysis of elastic-wave interaction with buried targets. We provide a detailed discussion on implementation of the perfectly matched layer and on treatment of the interface between two different materials. The algorithm has also been parallelized by the use of the message-passing interface. The numerical results show that numerical dispersion can be significantly improved by using biorthogonal wavelets as bases, as compared to the conventional pulse expansion employed in the finite-difference time-domain (FDTD) method. We demonstrate that with comparison to the second-order FDTD, the Bi-MRTD yields significant CPU time and memory savings for large problems, for a fixed level of accuracy.